The Perturbative Floquet Solution for Quasi-free Electrons

Abstract

In this paper the quasi-energies and the reduced Floquet vectors corresponding to a particle in 2-dimensions interacting with a time-dependent, monochromatic, linearly polarized electro-magnetic field, and in the presence of a weak, static, spatial-periodic field, are calculated. The later is treated using the stationary perturbation theory in the extended Hilbert space adapted for the eigenvalue equation of the Floquet Hamiltonian. The results have similarities to those of the quasi-free electron model.